The present invention generally relates to the field of quantitative phase analysis, and more specifically relates to a method for determining volume and/or weight fractions of different crystalline materials in a mixture using x-ray diffraction (XRD) techniques.
Most of the XRD-based quantitative phase analyses are based on the assumption that the measured diffraction intensity of the reflecting crystallographic planes of the sample is representative of all crystallographic planes of the same type (hkl), regardless of their orientation in the reciprocal space. However, when the sample comprises textured (i.e., having preferred crystallographic orientations) materials, the measurement result suffers from significant error, because the above-mentioned theoretical assumption is no longer true. In some cases, the error rate may be as high as 50% of the actual content of the estimated phase.
Special procedures therefore have been employed to eliminate or reduce the influence of texture on the results of XRD-based quantitative phase analysis.
For example, one may seek to mechanically eliminate texture, by grinding the sample into fine powder for preparation of a special sample. However, such approach requires complex sample preparation steps and results in complete destruction of the sample (D. L. Bish, J. E. Post, Modem Powder Diffraction, MSA, Washington, D.C., 1989, pp. 73-97).
Alternatively, one may seek to analytically eliminate texture, by using texture correction models for particles assumed to be either rod or disc shaped (A. March, Z. Kristallogr. 81, 1932, pp.285-297; W. A. Dollase, J. Appl. Cryst. 19, 1986, pp. 267-272). Those corrections apply to single component fiber textures and work relatively well for materials of weak textures. Other methods account for texture in the whole pattern refinement by describing the crystallite distribution by some analytical function (March (1932); Dollase (1986); P. Capkova, V. Valvoda, Czech J. Phys. 24, 1974, pp. 891-900).
The most advanced approach, i.e., the so-called Rietveld Texture Analysis (H. R. Wenk, S. Matthies, L. Lutterotti, Mat. Sci. Forum, Vol.157-162, 1994, pp. 473-480), uses numerous diffraction spectra collected at different sample orientations. It combines the crystallographic Rietveld refinement, the orientation distribution calculations, and some diffraction line broadening theories, and uses the least square fitting of a large number of multi-phase diffraction spectra, to obtain crystallographic texture and crystal structure information. The practical limitation of this method is that it requires collection of a very large number of diffraction spectra (often tens or hundreds for more complex materials), and takes long computation times (hours).
Experimentally, one may avoid the undesirable texture effects by selecting high multiplicity planes that produce x-ray diffraction peaks that are relatively insensitive to texture. This approach is based on experimental data obtained from careful calibration using a consistent set of samples, which is time-consuming. Moreover, this approach only works for sample materials of weak textures, and it is also vulnerable to calibration errors caused by variations of instrumental set-ups.
Another approach for eliminating texture influences from the XRD-based quantitative phase analysis involves determination of the Orientation Distribution Function (ODF) (H. J. Bunge, Texture Analysis in Materials Science, Butterworths, 1982), based on a set of experimental pole figures measured by x-ray diffraction and subsequent calculation of the pole density for each particular crystallographic reflection plane from the ODF. The calculated pole density is then used to correct the diffraction intensity measured in order to eliminate texture influences. In this approach, one pole figure is measured at a time, through a series of sample tilts with respect to the incident x-ray beam, which is time-consuming. One may also use one or more incomplete experimental pole figures and a direct method of the ODF calculation for the quantitative phase analysis, without collecting diffraction spectra in the 2"THgr" space (J. Bonarski, M. Wrobel, K. Pawlik, Scripta Metallurgica at Materialia, Vol. 25 (1991), pp. 1401-1404).
There are several methods that simplify the determination of the ODF, which include:
(a) making the orientation distribution cylindrically symmetrical, by spinning the sample around its normal, and then determining the symmetrical distribution from several pole distributions, wherein the ODF is described by spherical harmonic functions (P. M. de Wolf, W. H. Sas, Acta Cryst. A25, 1969, pp. 206-209; M. Jarvinen, M. Merisalo, A. Pesonen, O. Inkinen, J. Appl. Cryst. 3, 1970, pp. 313-318). However, this approach is not suitable for materials of sharp textures;
(b) measuring only the pole figures for a particular set of crystallographic planes (hkl) that are necessary for correction of the diffraction intensity Itexturedhkl from the (hkl) reflection. However, this approach requires either a combination of reflection and transmission techniques, or extrapolations of incomplete pole figures that may be incorrect;
(c) for fiber textures that are common in thin films and coatings, spinning the sample around its normal, so as to eliminate the "PHgr" variable (the azimuthal coordinate of the pole figure), and to determine the pole density Phkl(xcexa8) for the (hkl) reflection at various xcexa8 angles (radial, or pole coordinate of the pole figure). This approach is experimentally simpler, but it poses the problem of open-end normalization of the pole figures (V. Valvoda, Powder Diffraction, Vol.1, No.2, 1986, pp. 28-32);
It is therefore an advantage of the present invention to provide method and apparatus for fast and accurate quantitative phase analysis of highly textured polycrystalline materials, which rapidly and automatically collects and processes x-ray diffraction data for determining volume and/or weight fractions of textured polycrystalline materials of different phases in a mixture containing the same, while avoiding the above-described disadvantages or shortcomings of the conventional approaches.
Another advantage of the present invention involves elimination of the texture-caused measurement errors from the quantitative phase analysis results, without using complex sample preparation or numerous sample measurement steps that are necessary for conventional XRD-based quantitative phase analysis methods.
Other objects and advantages will be more fully apparent from the ensuing disclosure and appended claims.
The present invention relates to a method for quantitatively determining the phase composition of a sample mixture that comprises textured polycrystalline materials of multiple phases, such method comprising the steps of:
(a) collecting multiple incomplete pole figures for the multiple phases of the sample mixture, by steps that comprise:
(i) irradiating a measurement area on the sample mixture with radiation energy from a radiation source;
(ii) detecting the radiation energy diffracted from the sample mixture at a detection locus, wherein the detection locus is positioned in such a way as to capture a plurality of diffraction arcs within a single data capture frame; and
(iii) generating a diffraction image containing multiple incomplete pole figures for the multiple phases;
(b) calculating complete pole density distribution for a first set of crystallographic planes (hkl) of a first phase contained by the sample mixture, based on the incomplete pole figures collected on the diffraction image;
(c) correcting diffraction intensities collected on the diffraction image for the first set of crystallographic planes (hkl) of the first phase to eliminate crystallographic texture therefrom, by using the complete pole density distribution calculated in step (b);
(d) integrating the corrected values of diffraction intensities for the first set of crystallographic planes (hkl) of the first phase;
(e) repeating steps (b)-(d) to obtain integrated and corrected diffraction intensities for all phases contained by the sample mixture; and
(f) calculating the phase composition of the sample mixture from the corrected and integrated diffraction intensities obtained in steps (d) and (e).
In a preferred embodiment, the sample mixture comprises two textured polycrystalline materials whose crystal structures and lattice parameters are known. In an alternative embodiment, the sample mixture comprises more than two textured polycrystalline materials whose crystal structures and lattice parameters are known.
Another aspect of the present invention relates to a method for quantitatively determining phase composition of a sample mixture that comprises textured polycrystalline materials of multiple phases, said method comprising the steps of:
(a) collecting multiple incomplete pole figures for the multiple phases of the sample mixture, by steps that comprise:
(i) irradiating a measurement area on the sample mixture with radiation energy from a radiation source;
(ii) detecting the radiation energy diffracted from the sample mixture at a detection locus, wherein the detection locus is positioned in such a way as to capture a plurality of diffraction arcs within a single data capture frame; and
(iv) generating a diffraction image containing multiple incomplete pole figures for the multiple phases;
(b) averaging diffraction intensities collected on the diffraction image for a first set of crystallographic planes (hkl) of a first phase over all crystallographic orientations of the incomplete pole figures collected on the diffraction image;
(c) integrating the averaged values of diffraction intensities for the first set of crystallographic planes (hkl) of the first phase in step (b);
(d) correcting the integrated diffraction intensities in step (c) with a correction factor, which is the ratio of complete pole density distribution calculated from the incomplete pole figure over incomplete pole density distribution measured for the first set of crystallographic planes (hkl) of the first phase;
(e) repeating steps (b)-(d) to obtain integrated and corrected diffraction intensities for all phases contained by the sample mixture; and
(f) calculating the phase composition of the sample mixture from the corrected and integrated diffraction intensities obtained in steps (d) and (e).
Still another aspect of the present invention relates to a quantitative phase analysis system for determining the phase composition of a sample mixture that comprises textured polycrystalline materials of multiple phases, comprising:
a sample comprising a mixture of two or more textured polycrystalline materials, defining an associated sample plane;
a radiation source for directing radiation energy to a measurement area on the sample;
a 2-dimensional area detector that registers radiation energy diffracted from the sample at the measurement area, with the radiation source and the 2-dimensional area detector being in a fixed spatial relationship to one another and sufficiently proximate to the measurement area to capture a plurality of diffraction arcs within a single data capture frame of the area detector;
a sample motion assembly for translating the sample in the sample plane; and
a computer-based quantitative phase analyzer, constructed and arranged to collect and process diffraction data for determining the phase composition of the sample mixture.
Other aspects of the present invention will be more fully apparent from the ensuing disclosure and appended claims.